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Shreyans Sharma Grade: 11
        

Find ∫f(x)dx


If,


f[(3x-4)/3x+4)] = x+2

6 years ago

Answers : (2)

AKASH GOYAL AskiitiansExpert-IITD
419 Points
										

Dear Shreyans


first calculate f(x)


put 3x-4/3x+4 = y


calculate x in terms of y


x=4(1+y)/3(1-y)


x+2=2(5-y)/3(1-y) = 2(y-5)/3(y-1)


f(y)=2(y-5)/3(y-1)


f(x)=2(x-5)/3(x-1)


to integrate this use partial fractions


f(x)=2/3 [(x-1-4)/(x-1)]= 2/3[1 - 4/x-1]


now integration is simple


∫2/3[1 - 4/x-1]dx


2/3[x-4log(x-1)] + C


 


All the best.                                                           


AKASH GOYAL


AskiitiansExpert-IIT Delhi


 


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6 years ago
yash dalmia
18 Points
										

put 3x-4/3x+4=t,


on solving by componendo and dividendo,


6x/-8=t+1/t-1


x=4(t+1)/3(1-t)


put this in the given condition, get f(x), then integrate it

6 years ago
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